A Bayesian belief network includes nodes that are connected by directed edges or links. Each node represents a particular random variable having a certain number of states or values. Each link is directed from a parent node to a child node and shows the causal influence of the parent node on the child node. In particular, the link from a parent node to a child node represents a causal relationship between an event that occurred earlier, as indicated by the state of the parent node, and an event that occurred later, as indicated by the state of the child node.
Every child node in a belief network has an associated conditional probability distribution that describes the causal influence of its parents. The conditional probability distribution of a child node specifies one probability distribution for each combination of values of the parents of the child node. When all the nodes of a belief network are discrete, a conditional probability table (CPT) can represent the conditional probability distribution of each node. In a CPT, each row specifies the probability distribution of the child node, given a combination of states of the parent nodes. In addition to information stored in CPTs, which is based on prior knowledge, information regarding present or future events may be stored in the belief network in the form of evidence.
Using CPTs, and possibly evidence, beliefs can be computed for the nodes of the belief network. Beliefs represent conclusions that can be drawn about the present, using information about the past stored in the CPTs, and using information about the present stored in evidence, if any. A belief for a node X represents a conditional probability distribution of the node X, given all available evidence for that node.
To compute beliefs using a belief network, users of the belief network typically enter the CPT values for each node, based on the number of states of that node and on the number of parents that the node has. Such a process can become unwieldy, because the number of CPT values that must be specified for a node increases exponentially with the number of states and parents of the node.
There is a need for methods and systems that allow users of a belief network to generate CPTs more efficiently.